Developing long-term and network-wide timing-synchronization protocols that are energy-efficient represents one of the key strategies for the successful deployment of long-lived sensor networks. However, most of the existing protocols have focused only on achieving synchronization for short timescales, and are not appropriate for long-term synchronization. In the adaptive-clock synchronization protocols and, optimizing the network synchronization protocol was considered with the aim of achieving a specific synchronization accuracy with minimal energy consumption. The adaptive-clock synchronization protocol represents a probabilistic extension of RBS and proposes a mechanism for determining the minimum number of synchronization beacons and the synchronization rate in order to achieve a preestablished clock synchronization error. Ganeriwal et al. proposed for the first time a measurement-based study for designing an energy-efficient rate-adaptive long-time synchronization protocol (RATS) that adapts the synchronization period, number of beacons, and length of prediction window to achieve an applicationspecific accuracy.

Motivated in part by these preliminary contributions, we propose a more powerful AMTS scheme with the goal of achieving a long-term network-wide synchronization with minimal energy consumption. AMTS exhibits a number of attractive features:

• It represents a significantly enhanced extension of TPSN aiming at minimizing the overall energy consumption in large-scale and long-lived sensor networks.

• It is equipped with flexible mechanisms to adjust the synchronization mode, the period of network-wide timing synchronization (resynchronization rate), and schemes for joint estimation of clock offset and skew in order to achieve long-term reliability of synchronization.

• It employs a sequential message exchange technique and an energy-efficient signaling scheme to further reduce the energy consumption in synchronization procedures.

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